Computable Riesz Representation for the Dual of C[ 0; 1]

被引：0

作者：

Lu, Hong ^{[1
]}

Weihrauch, Klaus ^{[2
]}

机构：

[1] Nanjing Univ, Dept Math, Nanjing 21009, Jiangsu, Peoples R China

[2] Univ Hagen, Dept Math & Comp Sci, Hagen, Germany

来源：

ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE | 2007年 / 167卷

基金：

中国国家自然科学基金;

关键词：

Computable analysis; integration; Riesz representation theorem;

D O I：

10.1016/j.entcs.2006.08.012

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

By the Riesz representation theorem for the dual of C[ 0; 1], for every continuous linear operator F: C[ 0; 1] R there is a function g : [0; 1] R of bounded variation such that F(f) = integral f dg ( f is an element of C[ 0; 1]) The function g can be normalized such that V( g) = ||F|| In this paper we prove a computable version of this theorem. We use the framework of TTE, the representation approach to computable analysis, which allows to define natural computability for a variety of operators. We show that there are a computable operator S mapping g and an upper bound of its variation to F and a computable operator S (') mapping F and its norm to some appropriate g.

引用

页码：157 / 177

页数：21